Pressure-induced 0-$\pi$ transitions and supercurrent crossover in antiferromagnetic weak links

We compute self-consistently the Josephson current in a superconductor-antiferromagnet-superconductor junction using a lattice model, focusing on $0-\pi$ transitions occurring when the width of the antiferromagnetic region changes from an even to an odd number of lattice sites. Previous studies predicted $0-\pi$ transitions when alternating between an even and an odd number of sites for sufficiently strong antiferromagnetic order. We study numerically the magnitude of the threshold value for this to occur, and also explain the physics behind its existence in terms of the phase shifts picked up by the quasiparticles constituting the supercurrent in the antiferromagnet. Moreover, we show that this threshold value allows for pressure-induced $0-\pi$ transitions by destroying the antiferromagnetic nesting properties of the Fermi surface, a phenomenon which has no counterpart in ferromagnetic Josephson junctions, offering a way to tune the quantum ground state of a Josephson junction without the need for multiple samples.

Figure 1

Left panel: A model of the Josephson junction in the (110) direction. The red (blue) dots denote the $A$ ($B$) lattice. The dashed vertical line is the interface for an even junction, while the right solid line is the interface for an odd junction. The left solid line is the same for both even and odd junctions. Right panel: Critical current as a function of length $L$ for different values of the magnetic coupling constant $U$. The data are normalized to the $L=4$ value to simplify comparison. We have used $V=1.9$.

Figure 2

Critical value of the magnetic moment $m_c$ as a function of junction width $L$ for an antiferromagnetic junction (blue circles/diamonds) and a ferromagnetic junction (red squares). In the inset, the results plotted on a log-log scale for the ferromagnetic case fall on a straight line corresponding to $1/L$. The results for the antiferromagnetic case, however, saturate at large $L$. For the ferromagnetic case, the results show that for a wide enough SFS junction, any amount of ordering suffices to produce a $0-\pi$ transition in the junction. For the antiferromagnetic SAFS case, a threshold value is needed for this to occur, since only edge spins are uncompensated. We have used $V=1.9$.

Figure 3

Energy levels of current-carrying states of the system as a function of superconducting phase twist across the junction. The red lines denote spin-up states, and blue lines denote spin-down states. As the strength of the antiferromagnetic ordering increases ($U$ increases), spin-down states are lowered in energy by the Zeeman effect due to the uncompensated spin, while spin-up states increase in energy. Upper left panel: $U=0.5$. Upper right panel $U=1.2$. Lower left panel: $U=1.545$. Lower right panel: $U=2.0$. The contributions to the current are essentially determined by the $\varphi$ derivative of each of the curves. As the levels cross, the levels contributing most significantly to the current changes sign, leading to the $0-\pi$ transition. This requires a threshold value, unlike in the ferromagnetic case. Other parameter values are $V=1.9$, $\mu =0$, and $L=5$.